If you have a USA passport or other proof of citizenship then you are in the fortunate position of just being able to turn up and fly dual.
Yes, you can credit the hours. Any icao compliant training is creditable. It may not always be useful to credit it, apart from adding to your total hours but it is loggable/creditable. My UK ppl included a significant number of just this type of hours. Get the instructor to sign each line in your logbook and get a stamp from the flying club if you can.
At the solo stage, its all about flying, not nav/airspace, no reason why not to go and do some circuits/rejoins. If you are a dual citizen, you might just want a faa ppl anyway, and good comnfidence building experience to fly somewhere new.